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Convexity in Differential Games

In: Pareto Optimality, Game Theory And Equilibria

Author

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  • Valentin Ostapenko

    (National Technical University of Ukraine “Kyiv Polytechnical Institute”)

Abstract

The current chapter is devoted to the development of convex analysis concepts in the context of solving pursuit-evasion problems in differential games. Classic convex analysis is generalized; new concepts such as matrix-convex sets and H-convex sets are introduced and studied.With the help of these, it is shown possible to describe a rather wide class of differential games where players' strategies are produced in a comparatively constructive manner. The main attention is on studying those properties of matrix convexity that are required for the theory of differential games. Operational constructions for the initial positions sets, favorable to each player, for the derivation of the players' strategies are also described.

Suggested Citation

  • Valentin Ostapenko, 2008. "Convexity in Differential Games," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Athanasios Migdalas & Leonidas Pitsoulis (ed.), Pareto Optimality, Game Theory And Equilibria, pages 307-348, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-77247-9_12
    DOI: 10.1007/978-0-387-77247-9_12
    as

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